第二版《信息理论元素》：通信与电信领域的经典教材更新

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“Elements of Information Theory【英文版】，John A. Thomas” 《信息理论要素》第二版是该经典教材的最新更新版本，包含新的问题集和材料。本书继续保持清晰、启发思考的教学风格，结合数学、物理、统计和信息理论，为读者提供了一个全面的教育组合。所有信息理论的基本主题都得到了详尽的阐述，包括熵、数据压缩、信道容量、率失真理论、网络信息理论以及假设检验。作者旨在使读者深入理解理论基础及其应用。每章末尾的问题集和提要帮助读者巩固学习。章节后的历史注解回顾了主要内容。第二版的特点包括： 1. 重新组织的章节，优化教学流程。 2. 增加了200个新问题。 3. 新增源编码、投资组合理论和反馈容量的内容。 4. 更新了参考文献。现在，更新和增强的第二版《信息理论要素》仍然是电气工程、统计学和通信领域的本科高年级和研究生课程的理想教科书。教师手册提供了书中所有问题的详细解答，可从Wiley编辑部门获取。本书涵盖了信息理论的关键概念，如熵，它是衡量信息不确定性的度量；数据压缩，涉及如何在保持信息完整性的同时减少数据量；信道容量，定义了在给定的信噪比下，无错误传输的最大信息速率；率失真理论探讨了在允许一定质量损失的情况下如何最大限度地压缩信息；网络信息理论则研究多节点通信网络的信息处理和传输；而假设检验则用于确定观察到的数据是否支持特定的科学假设。通过深入学习这些概念，读者将能够理解和应用信息理论来解决实际问题，例如优化通信系统的效率、压缩数据以节省存储空间、设计有效的编码策略等。此外，书中引入的新材料如投资组合理论，将信息理论应用于金融领域，探讨如何在风险和回报之间找到平衡；反馈容量的讨论则涉及到反馈如何影响通信系统的性能。《信息理论要素》第二版是一本深入浅出、内容丰富的教材，不仅适合学术研究，也适用于专业实践，是任何对信息处理和通信技术感兴趣的学生或专业人士的宝贵资源。

PREFACE TO THE

SECOND EDITION

In the years since the publication of the ﬁrst edition, there were many

aspects of the book that we wished to improve, to rearrange, or to expand,

but the constraints of reprinting would not allow us to make those changes

between printings. In the new edition, we now get a chance to make some

of these changes, to add problems, and to discuss some topics that we had

omitted from the ﬁrst edition.

The key changes include a reorganization of the chapters to make

the book easier to teach, and the addition of more than two hundred

new problems. We have added material on universal portfolios, universal

source coding, Gaussian feedback capacity, network information theory,

and developed the duality of data compression and channel capacity. A

new chapter has been added and many proofs have been simpliﬁed. We

have also updated the references and historical notes.

The material in this book can be taught in a two-quarter sequence. The

ﬁrst quarter might cover Chapters 1 to 9, which includes the asymptotic

equipartition property, data compression, and channel capacity, culminat-

ing in the capacity of the Gaussian channel. The second quarter could

cover the remaining chapters, including rate distortion, the method of

types, Kolmogorov complexity, network information theory, universal

source coding, and portfolio theory. If only one semester is available, we

would add rate distortion and a single lecture each on Kolmogorov com-

plexity and network information theory to the ﬁrst semester. A web site,

http://www.elementsoﬁnformationtheory.com, provides links to additional

material and solutions to selected problems.

In the years since the ﬁrst edition of the book, information theory

celebrated its 50th birthday (the 50th anniversary of Shannon’s original

paper that started the ﬁeld), and ideas from information theory have been

applied to many problems of science and technology, including bioin-

formatics, web search, wireless communication, video compression, and

PREFACE TO THE

FIRST EDITION

This is intended to be a simple and accessible book on information theory.

As Einstein said, “Everything should be made as simple as possible, but no

simpler.” Although we have not veriﬁed the quote (ﬁrst found in a fortune

cookie), this point of view drives our development throughout the book.

There are a few key ideas and techniques that, when mastered, make the

subject appear simple and provide great intuition on new questions.

This book has arisen from over ten years of lectures in a two-quarter

sequence of a senior and ﬁrst-year graduate-level course in information

theory, and is intended as an introduction to information theory for stu-

dents of communication theory, computer science, and statistics.

There are two points to be made about the simplicities inherent in infor-

mation theory. First, certain quantities like entropy and mutual information

arise as the answers to fundamental questions. For example, entropy is

the minimum descriptive complexity of a random variable, and mutual

information is the communication rate in the presence of noise. Also,

as we shall point out, mutual information corresponds to the increase in

the doubling rate of wealth given side information. Second, the answers

to information theoretic questions have a natural algebraic structure. For

example, there is a chain rule for entropies, and entropy and mutual infor-

mation are related. Thus the answers to problems in data compression

and communication admit extensive interpretation. We all know the feel-

ing that follows when one investigates a problem, goes through a large

amount of algebra, and ﬁnally investigates the answer to ﬁnd that the

entire problem is illuminated not by the analysis but by the inspection of

the answer. Perhaps the outstanding examples of this in physics are New-

ton’s laws and Schr

odinger’s wave equation. Who could have foreseen the

awesome philosophical interpretations of Schr

odinger’s wave equation?

In the text we often investigate properties of the answer before we look

at the question. For example, in Chapter 2, we deﬁne entropy, relative

entropy, and mutual information and study the relationships and a few

xvii

xviii PREFACE TO THE FIRST EDITION

interpretations of them, showing how the answers ﬁt together in various

ways. Along the way we speculate on the meaning of the second law of

thermodynamics. Does entropy always increase? The answer is yes and

no. This is the sort of result that should please experts in the area but

might be overlooked as standard by the novice.

In fact, that brings up a point that often occurs in teaching. It is fun

to ﬁnd new proofs or slightly new results that no one else knows. When

one presents these ideas along with the established material in class, the

response is “sure, sure, sure.” But the excitement of teaching the material

is greatly enhanced. Thus we have derived great pleasure from investigat-

ing a number of new ideas in this textbook.

Examples of some of the new material in this text include the chapter

on the relationship of information theory to gambling, the work on the uni-

versality of the second law of thermodynamics in the context of Markov

chains, the joint typicality proofs of the channel capacity theorem, the

competitive optimality of Huffman codes, and the proof of Burg’s theorem

on maximum entropy spectral density estimation. Also, the chapter on

Kolmogorov complexity has no counterpart in other information theory

texts. We have also taken delight in relating Fisher information, mutual

information, the central limit theorem, and the Brunn–Minkowski and

entropy power inequalities. To our surprise, many of the classical results

on determinant inequalities are most easily proved using information the-

oretic inequalities.

Even though the ﬁeld of information theory has grown considerably

since Shannon’s original paper, we have strived to emphasize its coher-

ence. While it is clear that Shannon was motivated by problems in commu-

nication theory when he developed information theory, we treat informa-

tion theory as a ﬁeld of its own with applications to communication theory

and statistics. We were drawn to the ﬁeld of information theory from

backgrounds in communication theory, probability theory, and statistics,

because of the apparent impossibility of capturing the intangible concept

of information.

Since most of the results in the book are given as theorems and proofs,

we expect the elegance of the results to speak for themselves. In many

cases we actually describe the properties of the solutions before the prob-

lems. Again, the properties are interesting in themselves and provide a

natural rhythm for the proofs that follow.

One innovation in the presentation is our use of long chains of inequal-

ities with no intervening text followed immediately by the explanations.

By the time the reader comes to many of these proofs, we expect that he

or she will be able to follow most of these steps without any explanation

and will be able to pick out the needed explanations. These chains of

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第二版《信息理论元素》：通信与电信领域的经典教材更新

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